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If $\int \frac{\sqrt{\cot x}}{\sin xcos x} dx = P \sqrt{\cot x} + Q$ then the value of P⁴ is

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16

$\begin{array}{l} Let I = \int \frac{\sqrt{\cot x}}{\sin xcos x} dx = \int \frac{\sqrt{\cot x}}{\tan x} \sec^{2} xdx \\ = \int \frac{\sec^{2} x}{(\tan x)^{3 / 2}} dx = \frac{- 2}{\sqrt{\tan x}} + Q = - 2 \sqrt{\cot x} + Q \\ ∴ P = - 2 \Rightarrow P^{4} = 16 \end{array}$

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